Problem: Solve for $x$ and $y$ using elimination. ${-6x-y = -61}$ ${5x+y = 51}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-x = -10$ $\dfrac{-x}{{-1}} = \dfrac{-10}{{-1}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-6x-y = -61}\thinspace$ to find $y$ ${-6}{(10)}{ - y = -61}$ $-60-y = -61$ $-60{+60} - y = -61{+60}$ $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ You can also plug ${x = 10}$ into $\thinspace {5x+y = 51}\thinspace$ and get the same answer for $y$ : ${5}{(10)}{ + y = 51}$ ${y = 1}$